This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: STA 302 / 1001 F  Fall 2005 Test 2 November 16, 2005 LAST NAME: SOLUTIONS FIRST NAME: STUDENT NUMBER: ENROLLED IN: (circle one) STA 302 STA 1001 INSTRUCTIONS: • Time: 90 minutes • Aids allowed: calculator. • A table of values from the t distribution is on the second to last page (page 9). • A table of formulae is on the last page (page 10). • For all questions you can assume that the formulae on page 10 are known. • Total points: 44 1 2ab 2cd 3abc 3d 3efg 4 7 7 10 3 9 1 1. (4 points) Suppose that X is a 2 × 1 random vector with E( X ) = 1 2 ! and Cov( X ) = 4 1 1 9 ! . Y is another random vector with Y = AX where A is the constant matrix A = 12 3 ! . Find the expectation of Y and the variancecovariance matrix for Y . E( Y ) = A E( X ) = 12 3 ! 1 2 ! =3 6 ! Cov( Y ) = A Cov( X ) A = 12 3 ! 411 9 ! 12 3 ! = 6193 27 ! 12 3 ! = 445757 81 ! 2 2. (14 points) (a) Write the simple linear regression model in matrix terms, defining all terms. (3 marks) Y = X β + ² where Y = Y 1 Y 2 . . . Y n β = β β 1 ! X = 1 X 1 1 X 2 . . . . . . 1 X n ² = ² 1 ² 2 . . . ² n (b) Explain why Cov( ² ) = σ 2 I follows from the assumptions of simple linear regression. (4 marks) Cov ( ² ) is the n × n matrix with i th diagonal entry equal to the variance of ² i and ij th off diagonal entry equal to Cov ( ² i , ² j ) . Since two regression assumptions are that Var ( ² i ) = σ 2 for all i and Cov ( ² i , ² j ) = 0 , it follows that Cov ( ² ) = σ 2 I ....
View
Full Document
 Fall '04
 Gibbs
 Normal Distribution, Regression Analysis, Variance, Errors and residuals in statistics, QQ plot

Click to edit the document details